B-spline interpolation problem in Hilbert C∗-modules
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Published:2021-11-15
Issue:2
Volume:86
Page:275-298
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ISSN:0379-4024
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Container-title:Journal of Operator Theory
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language:
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Short-container-title:J. Operator Theory
Author:
Eskandari Rasoul, ,Frank Michael,Manuilov Vladimir M.,Moslehian Mohammad Sal, , ,
Abstract
We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on a Hilbert C∗-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when the Hilbert C∗-module is self-dual. Passing to the setting of Hilbert W∗-modules, we present our main result by characterizing when the spline interpolation problem for the extended C∗-valued sesquilinear form has a solution. Finally, solutions of the B-spline interpolation problem for Hilbert C∗-modules over C∗-ideals of W∗-algebras are extensively discussed.
Publisher
Theta Foundation
Subject
Algebra and Number Theory